Former France international has explained how he was able to help push the deal into fruition after meeting with the player
The 18-year-old centre-back is on his way to the capital city club after Lens president Gervais Martel revealed: "He will be playing for Real Madrid next season."
Manchester United, Lille and Paris Saint-Germain were also linked with the France Under-21 international, but Zidane believes his influence weighed upon the youngster's decision to join the club.
"I played an active role in the transfer. He is a quality player and has an incredible future ahead of him," Zidane told RMC.
"The fact that he saw Jose Mourinho was very important. This is the most important because he is the coach who will lead the team. They met. And essentially that's it."
Zidane, a former World Cup winner with France, lifted the trophy in 1998 alongside current national team boss Laurent Blanc.
And the ex-Juventus man can see similarities between Varane and his former international team-mate.
"I have watched plenty of Varane and he is like Blanc, fast, intelligent and he is a big player also," he concluded.
Varane scored two goals in 22 games last season as Lens were relegated into Ligue 2.